The census data states that one city has 52% women, 48% men, an average income o

Question

The census data states that one city has 52% women, 48% men, an average income of $45,000 with an SD of $30,000, and an average weight of 150 lbs, with an SD of 10. Assume that weights are normally distributed and that incomes are not. For all problems below, determine which test to use, and what test of use, and what type of SD would you use. a. You wish to test if the percent of women is correct, against the alternate that there is a lower percentage of women. You take a simple random sample of 10 people and find that 50% are women. b. You wish to test if the income is correct, against the alternate that the average is actually larger. You take a simple random sample of 10 people, which has an average $50,000 with an SD of $20,000. c. You wish to test if the weight is correct, against the alternative that the average is actually larger. You take a simple random sample of 10 people, which has an average weight of 155 lbs, with an SD of 15. d. You want to know if a district in the city has a larger average weight. You take a simple random sample of 10 people from the district, which has an average 155 with an SD of 15. Refer to the previous question. If we conduct the above tests with samples of 100 people instead of 10, all tests are z-tests. In that case, find the SD of the box for each of the above situations.

Explanation / Answer

Soln:

a)

We can get a rough approximation using z- test and then calculate p-value.

b)

No test we know applies and we can use t-test.

c)

Use t-test with SD+ from sample

d)

Use t-test with SD+ from sample

e)

1) (0.52*.48) ½ = 0.528

2) Sample SD = 20000

3) Sample SD = 15

4) Sample SD = 15

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